Thanks for the responses, folks. You've made me a little smarter on how UK rail works!
SanDiego1K -- AA is Terminal 3, roger that. I have the hyperlink bookmarked now. Thank you.
Aviatrix -- Thanks for the recommendation regarding the Piccadilly Line to St. Pancras--that didn't occur to me. I think we'll do that rather than using Heathrow Connect to avoid the train change in Paddington, and save a few pounds in the process. :-)
o0Herbie and Stut -- We are actually going to Long Eaton to go canaling (Sawley Marina), rather than Nottingham proper, so I guess we'll be paying the premium for the direct train. If I were a gambling man I'd try to cut costs by one of the alternate routes/combinations, but it's worth a little extra to avoid any surprises. Thanks for raising the point about engineering delays; we will try to factor those in to our planning.
I will plan on buying our rail tickets this weekend since the marina operator has recommended we get them ahead of time.
Meantime, if anyone has any further nuggets of wisdom I would be much obliged. Thanks again.
--Jon